for fear I'd make an educated guess at a les paul into a high gain marshall like a jcm800. alot of the low end from the guitar on that song comes fromt he cab he'd be playing through. nt many people running 4x12s in their bedrooms....

as for the dry county solo. I'd be prepared to bet he had some sort of boost for the solo to give that added gain and sustain but not totally overloading ont he treble. if it's not the boost he had on the old guitar then it's most probably come from a dirt pedal with the gain down and the level up. it's amazing how doing that can make harmonics jump off the fretboard with ease.